Hierarchy of rational order families of chaotic maps with an invariant measure

Jafarizadeh, M. A.; Foroutan, Masumeh; Ahadpour, Sodeif

doi:10.1007/s12043-006-0024-y

Cited by 9 publications

(6 citation statements)

References 17 publications

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“…In this section, we first review one-parameter chaotic maps that can be used as basis of chaotic trigonometric maps. The one-parameter chaotic maps are defined as the ratio of polynomials of degree N [22,23,24]:…”

Section:  Haar Waveletmentioning

confidence: 99%

Chaotic trigonometric Haar wavelet with focus on image encryption

Ahadpour

Sadra

2017

Journal of Discrete Mathematical Sciences and Cryptography

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In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling function of the Haar wavelet. With regard to applications of Haar wavelet transform in image processing, we introduce chaotic trigonometric Haar wavelet transform to encrypt the plain images. In addition, the encrypted images based on a proposed algorithm were made. To evaluate the security of the encrypted images, the key space analysis, the correlation coefficient analysis and differential attack were performed. Here, the chaotic trigonometric Haar wavelet transform tries to improve the problem of failure of encryption such as small key space and level of security.

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Section:  Haar Waveletmentioning

confidence: 99%

Chaotic trigonometric Haar wavelet with focus on image encryption

Ahadpour

Sadra

2017

Journal of Discrete Mathematical Sciences and Cryptography

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“…We first review one-parameter chaotic maps which can be used in the construction of chaotic trigonometric maps. The one-parameter chaotic maps [8] are defined as the ratio of polynomials of degree N: [8]. In order to simplify the calculation in this paper, we denote the chaotic trigonometric maps…”

Section: The Chaotic Trigonometricmentioning

confidence: 99%

Section: The Chaotic Trigonometricmentioning

confidence: 99%

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A Chaos-based Image Encryption Scheme using Chaotic Coupled Map Lattices

Ahadpour¹,

Sadra²

2012

IJCA

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In this letter, after reviewing the main points of the chaotic trigonometric maps and the coupled map lattices, we introduce the scheme of chaos-based image encryption based on coupled map lattices. The scheme decreases periodic effect of the ergodic dynamical systems in the chaos-based image encryption. To evaluate the security of the encrypted image of this scheme, the key space analysis, the correlation of two adjacent pixels and differential attack were performed. This scheme tries to improve the problem of failure of encryption such as small key space and level of security.

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“…1). Here in this paper we are concerned with their conjugate maps which are defined as: lead to the hierarchy of chaotic maps of trigonometric types (with an invariant measure), where some of them are equivalent to each others up to conjugacy [26]. …”

Section: Appendix a Definition Of Mapsmentioning

confidence: 99%